Video transcript

Which of the following real
numbers are irrational? Well, irrational just
means it's not rational. It means that you cannot
express it as the ratio of two integers. So let's see what we have here. So we have the square
root of 8 over 2. If you take the square root
of a number that is not a perfect square, it is
going to be irrational. And then if you just take
that irrational number and you multiply it, and you
divide it by any other numbers, you're still going to
get an irrational number. So square root of
8 is irrational. You divide that by 2,
it is still irrational. So this is not rational. Or in other words, I'm
saying it is irrational. Now, you have pi,
3.14159-- it just keeps going on and on and on
forever without ever repeating. So this is irrational,
probably the most famous of all of the
irrational numbers. 5.0-- well, I can
represent 5.0 as 5/1. So 5.0 is rational. It is not irrational. 0.325-- well, this is the
same thing as 325/1000. So I can clearly represent
it as a ratio of integers. So this is rational. Just as I could represent
5.0 as 5/1, both of these are rational. They are not irrational. Here I have
7.777777, and it just keeps going on and
on and on forever. And the way we denote
that, you could just say these dots that say
that the 7's keep going. Or you could say 7.7. And this line shows that
the 7 part, the second 7, just keeps repeating on forever. Now, if you have a repeating
decimal-- in other videos, we'll actually convert
them into fractions-- but a repeating decimal
can be represented as a ratio of two integers. Just as 1/3 is equal to
0.333 on and on and on. Or I could say it like this. I could say 3 repeating. We can also do the
same thing for that. I won't do it here,
but this is rational. So it's not irrational. 8 and 1/2? Well, that's the same thing. 8 and 1/2 is the
same thing as 17/2. So it's clearly rational. So the only two
irrational numbers are the first two
right over here.